BAGHDAD, July 27 -- The top U.S. military leader in Iraq said Wednesday there could be substantial withdrawals of some of the 135,000 U.S. troops in the country as early as next spring.

Gen. George W. Casey said that despite continued lethal attacks by insurgents, the security situation in Iraq had improved. He reiterated a position he had taken earlier this year on the possible decrease in the U.S. military presence during a one-day visit by Defense Secretary Donald H. Rumsfeld for meetings with Prime Minister Ibrahim Jafari.

Casey spoke on a day in which officials reported that 16 people were killed by insurgents, including two Algerian diplomats who had been kidnapped last week.

"If the political process continues to go positively, and if the development of the security forces continues to go as it is going, I do believe we'll still be able to take some fairly substantial reductions after these elections in the spring and summer," Casey said before meeting with Jafari.

While U.S. officials have said recently that troop cutbacks are possible, Rumsfeld's visit gave special focus to the prospects for withdrawals. Rumsfeld and other officials have rejected making a deadline public, but a secret British defense memo leaked this month in London said U.S. officials favored "a relatively bold reduction in force numbers."

Rumsfeld did not discuss troop levels specifically on Wednesday, but he linked the overall security situation to Iraqi military training and political progress toward completing a draft constitution by next month.

Failing to meet the deadline for passage of a new constitution "would be very harmful to the momentum that's necessary," Rumsfeld told reporters traveling with him to Baghdad. "We have troops on the ground there, people get killed," he said.

Iraqi leaders have also said consistently that U.S. troops should leave as soon as the U.S.-trained Iraqi army is ready to fight the insurgency and defend the country, but have estimated that it could take from 18 months to five years.

"The great desire of the Iraqi people is to see the coalition forces be on their way out as they take more responsibility," Jafari said at a news conference with Rumsfeld after their noon meeting in Baghdad.

But Jafari said a withdrawal would require "picking up the pace of training Iraqi forces," as well as carefully synchronizing the U.S. withdrawal as Iraqi forces took charge of different parts of the country.

"The withdrawal should be whenever the Iraqi forces are ready to stand up," Jafari said. "We don't want the Multinational Force to have a surprise departure.''

Earlier this month, a report prepared by Gen. Peter Pace, the incoming chairman of the Joint Chiefs of Staff, concluded that only a "small number" of Iraqi forces were capable of fighting insurgents without U.S. assistance.

Two-thirds of Iraqi forces are "partially capable'' of counterinsurgency missions if they have U.S. support, Pace concluded.

Since Jafari took office on April 28, there has been a marked escalation of insurgent attacks in Iraq. Daily death tolls from suicide bombings, ambushes and other attacks have been in the double digits most days this month.

In violence Wednesday, the insurgent group that calls itself al Qaeda in Iraq said it had killed two Algerian diplomats who were seized last week. Algerian President Abdelaziz Bouteflika called the killings of his country's chief envoy, Ali Belaroussi, and fellow diplomat Azzedine Belkadi "odious" and cowardly. He vowed to pursue the killers. Such kidnappings have driven many other Middle Eastern embassy officials to leave the country.

One U.S. soldier and six Iraqis were killed Wednesday in mortar attacks, bombings and ambushes, and Iraq's Defense Ministry reported that seven Iraqi soldiers had been killed by grenades and gunfire as they guarded a water plant Tuesday.

Casey suggested that the insurgency in Iraq was stagnating. "Insurgencies need progress to survive, and this insurgency is not progressing," he said. "What you're seeing is a change in tactics to more violent, more visible attacks against civilians, and that's a no-win strategy".

While insurgent violence is ongoing, Casey said, "the level of attacks they've been able to generate has not increased substantially over what we've seen over the past year."

A top U.S. commander in Iraq, Lt. Gen. John R. Vines, told reporters last month that four or five of 17 battalions, roughly one-quarter of U.S. forces in Iraq, could be pulled out if security conditions improved and if Iraqi national elections scheduled for December went smoothly.

The elections are supposed to follow an October referendum on the constitution. Iraqi Shiite, Sunni and Kurdish leaders negotiating the constitution still have major disagreements.

Rumsfeld said he discussed a number of military issues with officials related to increased Iraqi participation in security measures. He said the United States wants to train Iraqi guards so that prisoners and detainees can be transferred to Iraqi control. "Our hope," he said, is that "as soon as it's feasible we can transfer responsibility for Iraqi prisoners to the Iraqi government."

Rumsfeld said Iraqi leaders must also work on regional security and border issues.

"Iraq is a big country, an important country," he said. "They need to be aggressively communicating with their neighbors to see that foreign terrorists stop coming across those borders and that their neighbors do not harbor insurgents and finance insurgents is a way that is destructive."

He also said U.S. military lawyers were analyzing new legal arrangements to govern the status of U.S. forces in Iraq after new elections. The agreement could involve the extension of the current U.N. resolution regarding U.S. troops in Iraq, or a bilateral "status of forces" agreement. Such agreements with other countries also provide legal protections for U.S. forces abroad.

Giving U.S. forces legal immunity from Iraqi courts could be sensitive because of Iraqi concerns about killings involving innocent civilians. In particular, Jafari told reporters, he had asked Casey to investigate cases of "wrongful killing" by U.S. troops and to offer compensation and apologies where required.

Casey said the military would investigate such incidents occurring within the last 60 days. He added that U.S. officials would also examine additional training procedures for troops and compensation for property damage as well as accidental killings.